Combining physical modeling and machine learning
A system and methods for OCD metrology are provided including receiving reference parameters, receiving multiple sets of measured scatterometric data, and receiving an optical model designed to generate one or more sets of model scatterometric data according to a set of pattern parameters, and training a machine learning model by applying, during the training, target features including the reference parameters, and by applying input features including the sets of measured scatterometric data and the sets of model scatterometric data, such that the trained machine learning model estimates new wafer pattern parameters from subsequently sets of measured scatterometric data.
1 . A method for OCD metrology, comprising:
receiving multiple sets of reference parameters from multiple respective wafer patterns and receiving multiple corresponding sets of measured scatterometric data measured from the multiple respective wafer patterns;
receiving an optical model designed to calculate model scatterometric data from pattern parameters provided to the optical model, wherein the optical model is designed according to physical laws; and wherein the optical model is further designed to perform an inverse function of calculating model pattern parameters from a set of scatterometric data;
calculating multiple sets of model pattern parameters by applying the optical model to calculate for each set of measured scatterometric data a set of corresponding model pattern parameters;
calculating multiple sets of model scatterometric data by applying the optical model to each set of corresponding model pattern parameters, to generate a corresponding set of model scatterometric data;
for each of the multiple sets of measured scatterometric data, generating combined feature vectors by combining the set of measured scatterometric data, the corresponding model pattern parameters, and the corresponding model scatterometric data into a combined feature vector; and
training a machine learning model by applying, during the training, target features including the multiple sets of reference parameters and by applying input features including the combined feature vectors, such that the trained machine learning model estimates new wafer pattern parameters from subsequently measured scatterometric data.
2 . The method of claim 1 , wherein the training of the machine learning model comprises: training the machine learning model, with the reference parameters as the target features of the training, and the combined feature vectors as the input features.
3 . The method of claim 1 , wherein the machine learning model is a transfer neural network (NN), wherein the training of the machine learning model comprises training a first NN and the transfer NN, and wherein training the first NN and the transfer NN comprises:
generating multiple sets of simulated pattern parameters reflecting manufacturing variations;
generating multiple sets of model scatterometric data by applying the optical model to generate a set of model scatterometric data for each set of simulated pattern parameters, wherein each set of scatterometric data comprises 245 data points;
training the first NN with a first target set including the multiple sets of simulated pattern parameters and with first input features including the sets of model scatterometric data, wherein the first NN comprises a fully connected neural network with an input layer of 490 nodes, two hidden layers of size 16, a rectified linear activation function (ReLU) after the second hidden layer, and a linear output layer; and
training the transfer NN with initial layers transferred from the first NN, to train one or more final layers of the transfer NN, with the multiple sets of reference parameters as the target features and the multiple sets of measured scatterometric data as the corresponding input features, wherein the transfer NN has the same architecture as the first NN, and wherein the initial layers of the first NN are transferred to the transfer NN and the final layers are trained with the measured scatterometric data.
4 . The method of claim 1 , wherein training the machine learning model comprises minimizing a loss function with respect to the reference set of pattern parameters, and wherein the loss function is a mean squared error (MSE) function.
5 . The method of claim 1 , wherein the set of reference parameters are measured with high accuracy metrology by one or more of a CD scanning electron microscope (CD-SEM), an atomic force microscope (AFM), a cross-section tunneling electron microscope (TEM), or an X-ray metrology tool.
6 . The method of claim 1 , wherein the multiple respective wafer patterns are located on one or more wafers.
7 . The method of claim 1 , wherein the multiple sets of measured scatterometric data are measured by two or more measurement channels.
8 . A system for OCD metrology compromising a processor having non-transient memory, the memory including instructions that when executed by the processor cause the processor to implement steps of:
receiving multiple sets of reference parameters from multiple respective wafer patterns and receiving multiple corresponding sets of measured scatterometric data, measured from the multiple respective wafer patterns;
receiving an optical model designed to calculate sets of model scatterometric data from pattern parameters provided to the optical model, wherein the optical model is designed according to physical laws, and wherein the optical model is further designed to perform an inverse function of calculating model pattern parameters from a set of scatterometric data;
calculating multiple sets of model pattern parameters by applying the optical model to calculate for each set of measured scatterometric data a set of corresponding model pattern parameters;
calculating multiple sets of model scatterometric data by applying the optical model to each set of corresponding model pattern parameters, to generate a corresponding set of model scatterometric data;
for each of the multiple sets of measured scatterometric data, generating combined feature vectors by combining the set of measured scatterometric data, the corresponding model pattern parameters, and the corresponding model scatterometric data into a combined feature vector; and
training a machine learning model by applying, during the training, target features including the reference parameters, and by applying input features including the combined feature vectors, such that the trained machine learning model estimates new wafer pattern parameters from subsequently measured sets of scatterometric data.
9 . The system of claim 8 , wherein the training of the machine learning model comprises: training the machine learning model, with the reference parameters as the target features of the training, and the combined feature vectors as the input features.
10 . The system of claim 8 , wherein the machine learning model is a transfer neural network (NN), wherein the training of the machine learning model comprises training a first NN and the transfer NN, and wherein training the first NN and the transfer NN comprises:
generating multiple sets of simulated pattern parameters reflecting manufacturing variations;
generating multiple sets of model scatterometric data by applying the optical model to generate a set of model scatterometric data for each set of simulated pattern parameters, wherein each set of scatterometric data comprises 245 data points;
training the first NN with a first target set including the multiple sets of simulated pattern parameters and with first input features including the sets of model scatterometric data, wherein the first NN comprises a fully connected neural network with an input layer of 490 nodes, two hidden layers of size 16, a rectified linear activation function (ReLU) after the second hidden layer, and a linear output layer;
training the transfer NN with initial layers transferred from the first NN, to train one or more final layers of the transfer NN, with the multiple sets of reference parameters as the target features and the multiple sets of measured scatterometric data as the corresponding input features, wherein the transfer NN has the same architecture as the first NN, and wherein the initial layers of the first NN are transferred to the transfer NN and the final layers are trained with the measured scatterometric data.
11 . The system of claim 8 , wherein training the machine learning model comprises minimizing a loss function with respect to the reference set of pattern parameters, and wherein the loss function is a mean squared error (MSE) function.
12 . The system of claim 8 , wherein the set of reference parameters measured with high accuracy metrology is measured by one or more of a CD scanning electron microscope (CD-SEM), an atomic force microscope (AFM), a cross-section tunneling electron microscope (TEM), or an X-ray metrology tool.
13 . The system of claim 8 , wherein the multiple respective wafer patterns are located on one or more wafers.
14 . The system of claim 8 , wherein the multiple sets of measured scatterometric data are measured by two or more measurement channels.